Switch to a space of which you want to show the news to anonymous users. In your space tools, switch to the Permissions page. Set the permissions for anonymous users to at least "View all". Now the contents of this space, including news, will be visible to users who are not logged in. They still won't see contents from other spaces.

Delivering News for anonymous users

If anonymous users will be able to read news on your news pages, where you deliver them using one or more of Linchpin Enterprise News' macros, depends on those macros' configurations.

If they are configured to show those spaces you defined before as viewable by anonymous users, they will show up as usual.